A mathematical model to quantify the effects of probiotics
on the abundance of autochthonous intestinal bacteria
(This is a joint work with: Natalie Hemmerb, Katie Switzerb and Natalie Valdez-Vivasc,d)
a Department of Electrical and Computer Engineering, Texas A & M University,
b Department of Mathematics, Texas A & M University,
c Department of Economics, Texas A & M University,
d Department of European and Classical Languages and Cultures, Texas A & M University
Abstract: Probiotics are those bacteria that are believed to have beneficial effects on the health of animals and humans. It is thought that probiotics modify the composition and abundance of autochthonous intestinal bacteria. If this is true, probiotics may actually be useful in fighting disease and ultimately prolonging life. However, the nature of this phenomenon has been debated and is controversial. We have constructed a mathematical model in which the effects of probiotics on the composition of intestinal bacteria are simulated and quantified. This mathematical model consists of three differential equations demonstrating competitive and cooperative behaviors between existing bacteria in the intestine and the probiotics administered. We adapted our model from the competition and cooperation models; we also received data from a scientific study involving two adult dogs. In addition to the numerical simulations, we carried out a linear stability analysis to study the nature of the equilibrium points. When probitics are administered there can be a shift from one stable equilibrium to another. In fact, using the specific parameters values, this was the case. The experimental results primarily agreed with the results of the model analysis. These results indicate that probiotics has a notable impact on the ecology of intestinal bacteria. Nevertheless, any beneficial effects of these impacts has to be investigated in a separate study.
Modeling and Analysis of Coccidioidomycosis in the Endemic Regions of Texas: Effectiveness of Preventive Measures
(This is a joint work with: Amy Clantona , Laura Harredb, and Devin Lightd)
a,b,d Department of Mathematics, Texas A & M University,
c Department of Engineering, Texas A & M University
Abstract: Coccidioidomycosis is a growing concern in the U.S. as it has become endemic in many regions in the western hemisphere. There have been many controversial explanations as to why this is becoming a problem and how to prevent further spread of the disease. Considering dogs to be the most commonly infected after humans, we constructed a model to simulate the impact of avoiding the burial of dogs in shallow graves using data from Webb County, an endemic region in Texas. We used a system of five nonlinear differential equations and found the numerical solutions to the equations for different values of the burial rate. We used the data to estimate the transmission rates. The linear stability of the disease free equilibrium and the effects of parameter changes was studied. Using the symbolic toolbox of Matlab, the endemic equilibrium was obtained; nevertheless the stability analysis of the endemic equilibrium remains an open problem. By varying burial and transmission rates, our model indicates that, if implemented correctly, burial avoidance may significantly reduce the number of infected dogs. Nonetheless, the disease will persist in the host population, when the transmission rates are high. Hence, burial avoidance would be a more effective measure if it was combined with other preventive measures.
Modeling Optimal Area of Cooling Zones Following a Marathon
(This is a joint work with: Matthew Fergusona, Matthew Foster b,and Siamak Narimanb)
a. Department of Mathematics, Texas A&M University
b. Department of Electrical Engineering, Texas A&M University
Abstract: This study aims to resolve overcrowding issues in marathons by determining the optimal area needed for each of two cooling zones to manage racer population fluctuations. We developed a modeling approach by transforming data from previous races into an appropriate distribution of finish times, in order to better organize future events. Specifically, three different models were constructed. The first two models were rejected due to naive assumptions and outcome predictions. The final model was the most accurate, in which we used a density dependent traffic flow that is dependent to the number of people in each cooling zone. In this case, when the population is large, there is still a consistent outflow. This model accurately predicts the changes in the population of each cooling zone and it is stable to variations in delay terms. Using the curve fitting and parameter estimation we obtained feasible explanations of actual occurrences in a post-marathon expo. Moreover, by numerical simulations of the the model, we obtained the percentage of allotted area for both of the cooling zones with the goal of providing the most efficient allocation of space.
Date: Monday April 25
Time: 7:00-8:00 pm
Location: 164 Blocker
Mathematical Modeling and Analysis
Hosted by Math Club